// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2008-2009 Benoit Jacob <jacob.benoit.1@gmail.com>
// Copyright (C) 2009 Kenneth Riddile <kfriddile@yahoo.com>
// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
// Copyright (C) 2010 Thomas Capricelli <orzel@freehackers.org>
// Copyright (C) 2013 Pavel Holoborodko <pavel@holoborodko.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

/*****************************************************************************
*** Platform checks for aligned malloc functions                           ***
*****************************************************************************/

#ifndef EIGEN_MEMORY_H
#define EIGEN_MEMORY_H

#ifndef EIGEN_MALLOC_ALREADY_ALIGNED

// Try to determine automatically if malloc is already aligned.

// On 64-bit systems, glibc's malloc returns 16-byte-aligned pointers, see:
//   http://www.gnu.org/s/libc/manual/html_node/Aligned-Memory-Blocks.html
// This is true at least since glibc 2.8.
// This leaves the question how to detect 64-bit. According to this document,
//   http://gcc.fyxm.net/summit/2003/Porting%20to%2064%20bit.pdf
// page 114, "[The] LP64 model [...] is used by all 64-bit UNIX ports" so it's indeed
// quite safe, at least within the context of glibc, to equate 64-bit with LP64.
#if defined(__GLIBC__) && ((__GLIBC__ >= 2 && __GLIBC_MINOR__ >= 8) || __GLIBC__ > 2) && defined(__LP64__) &&          \
	!defined(__SANITIZE_ADDRESS__) && (EIGEN_DEFAULT_ALIGN_BYTES == 16)
#define EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED 1
#else
#define EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED 0
#endif

// FreeBSD 6 seems to have 16-byte aligned malloc
//   See http://svn.freebsd.org/viewvc/base/stable/6/lib/libc/stdlib/malloc.c?view=markup
// FreeBSD 7 seems to have 16-byte aligned malloc except on ARM and MIPS architectures
//   See http://svn.freebsd.org/viewvc/base/stable/7/lib/libc/stdlib/malloc.c?view=markup
#if defined(__FreeBSD__) && !(EIGEN_ARCH_ARM || EIGEN_ARCH_MIPS) && (EIGEN_DEFAULT_ALIGN_BYTES == 16)
#define EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED 1
#else
#define EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED 0
#endif

#if (EIGEN_OS_MAC && (EIGEN_DEFAULT_ALIGN_BYTES == 16)) || (EIGEN_OS_WIN64 && (EIGEN_DEFAULT_ALIGN_BYTES == 16)) ||    \
	EIGEN_GLIBC_MALLOC_ALREADY_ALIGNED || EIGEN_FREEBSD_MALLOC_ALREADY_ALIGNED
#define EIGEN_MALLOC_ALREADY_ALIGNED 1
#else
#define EIGEN_MALLOC_ALREADY_ALIGNED 0
#endif

#endif

namespace Eigen {

namespace internal {

EIGEN_DEVICE_FUNC
inline void
throw_std_bad_alloc()
{
#ifdef EIGEN_EXCEPTIONS
	throw std::bad_alloc();
#else
	std::size_t huge = static_cast<std::size_t>(-1);
#if defined(EIGEN_HIPCC)
	//
	// calls to "::operator new" are to be treated as opaque function calls (i.e no inlining),
	// and as a consequence the code in the #else block triggers the hipcc warning :
	// "no overloaded function has restriction specifiers that are compatible with the ambient context"
	//
	// "throw_std_bad_alloc" has the EIGEN_DEVICE_FUNC attribute, so it seems that hipcc expects
	// the same on "operator new"
	// Reverting code back to the old version in this #if block for the hipcc compiler
	//
	new int[huge];
#else
	void* unused = ::operator new(huge);
	EIGEN_UNUSED_VARIABLE(unused);
#endif
#endif
}

/*****************************************************************************
*** Implementation of handmade aligned functions                           ***
*****************************************************************************/

/* ----- Hand made implementations of aligned malloc/free and realloc ----- */

/** \internal Like malloc, but the returned pointer is guaranteed to be 16-byte aligned.
 * Fast, but wastes 16 additional bytes of memory. Does not throw any exception.
 */
EIGEN_DEVICE_FUNC inline void*
handmade_aligned_malloc(std::size_t size, std::size_t alignment = EIGEN_DEFAULT_ALIGN_BYTES)
{
	eigen_assert(alignment >= sizeof(void*) && (alignment & (alignment - 1)) == 0 &&
				 "Alignment must be at least sizeof(void*) and a power of 2");

	EIGEN_USING_STD(malloc)
	void* original = malloc(size + alignment);

	if (original == 0)
		return 0;
	void* aligned =
		reinterpret_cast<void*>((reinterpret_cast<std::size_t>(original) & ~(std::size_t(alignment - 1))) + alignment);
	*(reinterpret_cast<void**>(aligned) - 1) = original;
	return aligned;
}

/** \internal Frees memory allocated with handmade_aligned_malloc */
EIGEN_DEVICE_FUNC inline void
handmade_aligned_free(void* ptr)
{
	if (ptr) {
		EIGEN_USING_STD(free)
		free(*(reinterpret_cast<void**>(ptr) - 1));
	}
}

/** \internal
 * \brief Reallocates aligned memory.
 * Since we know that our handmade version is based on std::malloc
 * we can use std::realloc to implement efficient reallocation.
 */
inline void*
handmade_aligned_realloc(void* ptr, std::size_t size, std::size_t = 0)
{
	if (ptr == 0)
		return handmade_aligned_malloc(size);
	void* original = *(reinterpret_cast<void**>(ptr) - 1);
	std::ptrdiff_t previous_offset = static_cast<char*>(ptr) - static_cast<char*>(original);
	original = std::realloc(original, size + EIGEN_DEFAULT_ALIGN_BYTES);
	if (original == 0)
		return 0;
	void* aligned = reinterpret_cast<void*>(
		(reinterpret_cast<std::size_t>(original) & ~(std::size_t(EIGEN_DEFAULT_ALIGN_BYTES - 1))) +
		EIGEN_DEFAULT_ALIGN_BYTES);
	void* previous_aligned = static_cast<char*>(original) + previous_offset;
	if (aligned != previous_aligned)
		std::memmove(aligned, previous_aligned, size);

	*(reinterpret_cast<void**>(aligned) - 1) = original;
	return aligned;
}

/*****************************************************************************
*** Implementation of portable aligned versions of malloc/free/realloc     ***
*****************************************************************************/

#ifdef EIGEN_NO_MALLOC
EIGEN_DEVICE_FUNC inline void
check_that_malloc_is_allowed()
{
	eigen_assert(false && "heap allocation is forbidden (EIGEN_NO_MALLOC is defined)");
}
#elif defined EIGEN_RUNTIME_NO_MALLOC
EIGEN_DEVICE_FUNC inline bool
is_malloc_allowed_impl(bool update, bool new_value = false)
{
	static bool value = true;
	if (update == 1)
		value = new_value;
	return value;
}
EIGEN_DEVICE_FUNC inline bool
is_malloc_allowed()
{
	return is_malloc_allowed_impl(false);
}
EIGEN_DEVICE_FUNC inline bool
set_is_malloc_allowed(bool new_value)
{
	return is_malloc_allowed_impl(true, new_value);
}
EIGEN_DEVICE_FUNC inline void
check_that_malloc_is_allowed()
{
	eigen_assert(is_malloc_allowed() &&
				 "heap allocation is forbidden (EIGEN_RUNTIME_NO_MALLOC is defined and g_is_malloc_allowed is false)");
}
#else
EIGEN_DEVICE_FUNC inline void
check_that_malloc_is_allowed()
{
}
#endif

/** \internal Allocates \a size bytes. The returned pointer is guaranteed to have 16 or 32 bytes alignment depending on
 * the requirements. On allocation error, the returned pointer is null, and std::bad_alloc is thrown.
 */
EIGEN_DEVICE_FUNC inline void*
aligned_malloc(std::size_t size)
{
	check_that_malloc_is_allowed();

	void* result;
#if (EIGEN_DEFAULT_ALIGN_BYTES == 0) || EIGEN_MALLOC_ALREADY_ALIGNED

	EIGEN_USING_STD(malloc)
	result = malloc(size);

#if EIGEN_DEFAULT_ALIGN_BYTES == 16
	eigen_assert((size < 16 || (std::size_t(result) % 16) == 0) &&
				 "System's malloc returned an unaligned pointer. Compile with EIGEN_MALLOC_ALREADY_ALIGNED=0 to "
				 "fallback to handmade aligned memory allocator.");
#endif
#else
	result = handmade_aligned_malloc(size);
#endif

	if (!result && size)
		throw_std_bad_alloc();

	return result;
}

/** \internal Frees memory allocated with aligned_malloc. */
EIGEN_DEVICE_FUNC inline void
aligned_free(void* ptr)
{
#if (EIGEN_DEFAULT_ALIGN_BYTES == 0) || EIGEN_MALLOC_ALREADY_ALIGNED

	EIGEN_USING_STD(free)
	free(ptr);

#else
	handmade_aligned_free(ptr);
#endif
}

/**
 * \internal
 * \brief Reallocates an aligned block of memory.
 * \throws std::bad_alloc on allocation failure
 */
inline void*
aligned_realloc(void* ptr, std::size_t new_size, std::size_t old_size)
{
	EIGEN_UNUSED_VARIABLE(old_size)

	void* result;
#if (EIGEN_DEFAULT_ALIGN_BYTES == 0) || EIGEN_MALLOC_ALREADY_ALIGNED
	result = std::realloc(ptr, new_size);
#else
	result = handmade_aligned_realloc(ptr, new_size, old_size);
#endif

	if (!result && new_size)
		throw_std_bad_alloc();

	return result;
}

/*****************************************************************************
*** Implementation of conditionally aligned functions                      ***
*****************************************************************************/

/** \internal Allocates \a size bytes. If Align is true, then the returned ptr is 16-byte-aligned.
 * On allocation error, the returned pointer is null, and a std::bad_alloc is thrown.
 */
template<bool Align>
EIGEN_DEVICE_FUNC inline void*
conditional_aligned_malloc(std::size_t size)
{
	return aligned_malloc(size);
}

template<>
EIGEN_DEVICE_FUNC inline void*
conditional_aligned_malloc<false>(std::size_t size)
{
	check_that_malloc_is_allowed();

	EIGEN_USING_STD(malloc)
	void* result = malloc(size);

	if (!result && size)
		throw_std_bad_alloc();
	return result;
}

/** \internal Frees memory allocated with conditional_aligned_malloc */
template<bool Align>
EIGEN_DEVICE_FUNC inline void
conditional_aligned_free(void* ptr)
{
	aligned_free(ptr);
}

template<>
EIGEN_DEVICE_FUNC inline void
conditional_aligned_free<false>(void* ptr)
{
	EIGEN_USING_STD(free)
	free(ptr);
}

template<bool Align>
inline void*
conditional_aligned_realloc(void* ptr, std::size_t new_size, std::size_t old_size)
{
	return aligned_realloc(ptr, new_size, old_size);
}

template<>
inline void*
conditional_aligned_realloc<false>(void* ptr, std::size_t new_size, std::size_t)
{
	return std::realloc(ptr, new_size);
}

/*****************************************************************************
*** Construction/destruction of array elements                             ***
*****************************************************************************/

/** \internal Destructs the elements of an array.
 * The \a size parameters tells on how many objects to call the destructor of T.
 */
template<typename T>
EIGEN_DEVICE_FUNC inline void
destruct_elements_of_array(T* ptr, std::size_t size)
{
	// always destruct an array starting from the end.
	if (ptr)
		while (size)
			ptr[--size].~T();
}

/** \internal Constructs the elements of an array.
 * The \a size parameter tells on how many objects to call the constructor of T.
 */
template<typename T>
EIGEN_DEVICE_FUNC inline T*
construct_elements_of_array(T* ptr, std::size_t size)
{
	std::size_t i;
	EIGEN_TRY
	{
		for (i = 0; i < size; ++i)
			::new (ptr + i) T;
		return ptr;
	}
	EIGEN_CATCH(...)
	{
		destruct_elements_of_array(ptr, i);
		EIGEN_THROW;
	}
	return NULL;
}

/*****************************************************************************
*** Implementation of aligned new/delete-like functions                    ***
*****************************************************************************/

template<typename T>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void
check_size_for_overflow(std::size_t size)
{
	if (size > std::size_t(-1) / sizeof(T))
		throw_std_bad_alloc();
}

/** \internal Allocates \a size objects of type T. The returned pointer is guaranteed to have 16 bytes alignment.
 * On allocation error, the returned pointer is undefined, but a std::bad_alloc is thrown.
 * The default constructor of T is called.
 */
template<typename T>
EIGEN_DEVICE_FUNC inline T*
aligned_new(std::size_t size)
{
	check_size_for_overflow<T>(size);
	T* result = reinterpret_cast<T*>(aligned_malloc(sizeof(T) * size));
	EIGEN_TRY
	{
		return construct_elements_of_array(result, size);
	}
	EIGEN_CATCH(...)
	{
		aligned_free(result);
		EIGEN_THROW;
	}
	return result;
}

template<typename T, bool Align>
EIGEN_DEVICE_FUNC inline T*
conditional_aligned_new(std::size_t size)
{
	check_size_for_overflow<T>(size);
	T* result = reinterpret_cast<T*>(conditional_aligned_malloc<Align>(sizeof(T) * size));
	EIGEN_TRY
	{
		return construct_elements_of_array(result, size);
	}
	EIGEN_CATCH(...)
	{
		conditional_aligned_free<Align>(result);
		EIGEN_THROW;
	}
	return result;
}

/** \internal Deletes objects constructed with aligned_new
 * The \a size parameters tells on how many objects to call the destructor of T.
 */
template<typename T>
EIGEN_DEVICE_FUNC inline void
aligned_delete(T* ptr, std::size_t size)
{
	destruct_elements_of_array<T>(ptr, size);
	Eigen::internal::aligned_free(ptr);
}

/** \internal Deletes objects constructed with conditional_aligned_new
 * The \a size parameters tells on how many objects to call the destructor of T.
 */
template<typename T, bool Align>
EIGEN_DEVICE_FUNC inline void
conditional_aligned_delete(T* ptr, std::size_t size)
{
	destruct_elements_of_array<T>(ptr, size);
	conditional_aligned_free<Align>(ptr);
}

template<typename T, bool Align>
EIGEN_DEVICE_FUNC inline T*
conditional_aligned_realloc_new(T* pts, std::size_t new_size, std::size_t old_size)
{
	check_size_for_overflow<T>(new_size);
	check_size_for_overflow<T>(old_size);
	if (new_size < old_size)
		destruct_elements_of_array(pts + new_size, old_size - new_size);
	T* result = reinterpret_cast<T*>(
		conditional_aligned_realloc<Align>(reinterpret_cast<void*>(pts), sizeof(T) * new_size, sizeof(T) * old_size));
	if (new_size > old_size) {
		EIGEN_TRY
		{
			construct_elements_of_array(result + old_size, new_size - old_size);
		}
		EIGEN_CATCH(...)
		{
			conditional_aligned_free<Align>(result);
			EIGEN_THROW;
		}
	}
	return result;
}

template<typename T, bool Align>
EIGEN_DEVICE_FUNC inline T*
conditional_aligned_new_auto(std::size_t size)
{
	if (size == 0)
		return 0; // short-cut. Also fixes Bug 884
	check_size_for_overflow<T>(size);
	T* result = reinterpret_cast<T*>(conditional_aligned_malloc<Align>(sizeof(T) * size));
	if (NumTraits<T>::RequireInitialization) {
		EIGEN_TRY
		{
			construct_elements_of_array(result, size);
		}
		EIGEN_CATCH(...)
		{
			conditional_aligned_free<Align>(result);
			EIGEN_THROW;
		}
	}
	return result;
}

template<typename T, bool Align>
inline T*
conditional_aligned_realloc_new_auto(T* pts, std::size_t new_size, std::size_t old_size)
{
	check_size_for_overflow<T>(new_size);
	check_size_for_overflow<T>(old_size);
	if (NumTraits<T>::RequireInitialization && (new_size < old_size))
		destruct_elements_of_array(pts + new_size, old_size - new_size);
	T* result = reinterpret_cast<T*>(
		conditional_aligned_realloc<Align>(reinterpret_cast<void*>(pts), sizeof(T) * new_size, sizeof(T) * old_size));
	if (NumTraits<T>::RequireInitialization && (new_size > old_size)) {
		EIGEN_TRY
		{
			construct_elements_of_array(result + old_size, new_size - old_size);
		}
		EIGEN_CATCH(...)
		{
			conditional_aligned_free<Align>(result);
			EIGEN_THROW;
		}
	}
	return result;
}

template<typename T, bool Align>
EIGEN_DEVICE_FUNC inline void
conditional_aligned_delete_auto(T* ptr, std::size_t size)
{
	if (NumTraits<T>::RequireInitialization)
		destruct_elements_of_array<T>(ptr, size);
	conditional_aligned_free<Align>(ptr);
}

/****************************************************************************/

/** \internal Returns the index of the first element of the array that is well aligned with respect to the requested \a
 * Alignment.
 *
 * \tparam Alignment requested alignment in Bytes.
 * \param array the address of the start of the array
 * \param size the size of the array
 *
 * \note If no element of the array is well aligned or the requested alignment is not a multiple of a scalar,
 * the size of the array is returned. For example with SSE, the requested alignment is typically 16-bytes. If
 * packet size for the given scalar type is 1, then everything is considered well-aligned.
 *
 * \note Otherwise, if the Alignment is larger that the scalar size, we rely on the assumptions that sizeof(Scalar) is a
 * power of 2. On the other hand, we do not assume that the array address is a multiple of sizeof(Scalar), as that fails
 * for example with Scalar=double on certain 32-bit platforms, see bug #79.
 *
 * There is also the variant first_aligned(const MatrixBase&) defined in DenseCoeffsBase.h.
 * \sa first_default_aligned()
 */
template<int Alignment, typename Scalar, typename Index>
EIGEN_DEVICE_FUNC inline Index
first_aligned(const Scalar* array, Index size)
{
	const Index ScalarSize = sizeof(Scalar);
	const Index AlignmentSize = Alignment / ScalarSize;
	const Index AlignmentMask = AlignmentSize - 1;

	if (AlignmentSize <= 1) {
		// Either the requested alignment if smaller than a scalar, or it exactly match a 1 scalar
		// so that all elements of the array have the same alignment.
		return 0;
	} else if ((UIntPtr(array) & (sizeof(Scalar) - 1)) || (Alignment % ScalarSize) != 0) {
		// The array is not aligned to the size of a single scalar, or the requested alignment is not a multiple of the
		// scalar size. Consequently, no element of the array is well aligned.
		return size;
	} else {
		Index first = (AlignmentSize - (Index((UIntPtr(array) / sizeof(Scalar))) & AlignmentMask)) & AlignmentMask;
		return (first < size) ? first : size;
	}
}

/** \internal Returns the index of the first element of the array that is well aligned with respect the largest packet
 * requirement. \sa first_aligned(Scalar*,Index) and first_default_aligned(DenseBase<Derived>) */
template<typename Scalar, typename Index>
EIGEN_DEVICE_FUNC inline Index
first_default_aligned(const Scalar* array, Index size)
{
	typedef typename packet_traits<Scalar>::type DefaultPacketType;
	return first_aligned<unpacket_traits<DefaultPacketType>::alignment>(array, size);
}

/** \internal Returns the smallest integer multiple of \a base and greater or equal to \a size
 */
template<typename Index>
inline Index
first_multiple(Index size, Index base)
{
	return ((size + base - 1) / base) * base;
}

// std::copy is much slower than memcpy, so let's introduce a smart_copy which
// use memcpy on trivial types, i.e., on types that does not require an initialization ctor.
template<typename T, bool UseMemcpy>
struct smart_copy_helper;

template<typename T>
EIGEN_DEVICE_FUNC void
smart_copy(const T* start, const T* end, T* target)
{
	smart_copy_helper<T, !NumTraits<T>::RequireInitialization>::run(start, end, target);
}

template<typename T>
struct smart_copy_helper<T, true>
{
	EIGEN_DEVICE_FUNC static inline void run(const T* start, const T* end, T* target)
	{
		IntPtr size = IntPtr(end) - IntPtr(start);
		if (size == 0)
			return;
		eigen_internal_assert(start != 0 && end != 0 && target != 0);
		EIGEN_USING_STD(memcpy)
		memcpy(target, start, size);
	}
};

template<typename T>
struct smart_copy_helper<T, false>
{
	EIGEN_DEVICE_FUNC static inline void run(const T* start, const T* end, T* target) { std::copy(start, end, target); }
};

// intelligent memmove. falls back to std::memmove for POD types, uses std::copy otherwise.
template<typename T, bool UseMemmove>
struct smart_memmove_helper;

template<typename T>
void
smart_memmove(const T* start, const T* end, T* target)
{
	smart_memmove_helper<T, !NumTraits<T>::RequireInitialization>::run(start, end, target);
}

template<typename T>
struct smart_memmove_helper<T, true>
{
	static inline void run(const T* start, const T* end, T* target)
	{
		IntPtr size = IntPtr(end) - IntPtr(start);
		if (size == 0)
			return;
		eigen_internal_assert(start != 0 && end != 0 && target != 0);
		std::memmove(target, start, size);
	}
};

template<typename T>
struct smart_memmove_helper<T, false>
{
	static inline void run(const T* start, const T* end, T* target)
	{
		if (UIntPtr(target) < UIntPtr(start)) {
			std::copy(start, end, target);
		} else {
			std::ptrdiff_t count = (std::ptrdiff_t(end) - std::ptrdiff_t(start)) / sizeof(T);
			std::copy_backward(start, end, target + count);
		}
	}
};

#if EIGEN_HAS_RVALUE_REFERENCES
template<typename T>
EIGEN_DEVICE_FUNC T*
smart_move(T* start, T* end, T* target)
{
	return std::move(start, end, target);
}
#else
template<typename T>
EIGEN_DEVICE_FUNC T*
smart_move(T* start, T* end, T* target)
{
	return std::copy(start, end, target);
}
#endif

/*****************************************************************************
*** Implementation of runtime stack allocation (falling back to malloc)    ***
*****************************************************************************/

// you can overwrite Eigen's default behavior regarding alloca by defining EIGEN_ALLOCA
// to the appropriate stack allocation function
#if !defined EIGEN_ALLOCA && !defined EIGEN_GPU_COMPILE_PHASE
#if EIGEN_OS_LINUX || EIGEN_OS_MAC || (defined alloca)
#define EIGEN_ALLOCA alloca
#elif EIGEN_COMP_MSVC
#define EIGEN_ALLOCA _alloca
#endif
#endif

// With clang -Oz -mthumb, alloca changes the stack pointer in a way that is
// not allowed in Thumb2. -DEIGEN_STACK_ALLOCATION_LIMIT=0 doesn't work because
// the compiler still emits bad code because stack allocation checks use "<=".
// TODO: Eliminate after https://bugs.llvm.org/show_bug.cgi?id=23772
// is fixed.
#if defined(__clang__) && defined(__thumb__)
#undef EIGEN_ALLOCA
#endif

// This helper class construct the allocated memory, and takes care of destructing and freeing the handled data
// at destruction time. In practice this helper class is mainly useful to avoid memory leak in case of exceptions.
template<typename T>
class aligned_stack_memory_handler : noncopyable
{
  public:
	/* Creates a stack_memory_handler responsible for the buffer \a ptr of size \a size.
	 * Note that \a ptr can be 0 regardless of the other parameters.
	 * This constructor takes care of constructing/initializing the elements of the buffer if required by the scalar
	 *type T (see NumTraits<T>::RequireInitialization). In this case, the buffer elements will also be destructed when
	 *this handler will be destructed. Finally, if \a dealloc is true, then the pointer \a ptr is freed.
	 **/
	EIGEN_DEVICE_FUNC
	aligned_stack_memory_handler(T* ptr, std::size_t size, bool dealloc)
		: m_ptr(ptr)
		, m_size(size)
		, m_deallocate(dealloc)
	{
		if (NumTraits<T>::RequireInitialization && m_ptr)
			Eigen::internal::construct_elements_of_array(m_ptr, size);
	}
	EIGEN_DEVICE_FUNC
	~aligned_stack_memory_handler()
	{
		if (NumTraits<T>::RequireInitialization && m_ptr)
			Eigen::internal::destruct_elements_of_array<T>(m_ptr, m_size);
		if (m_deallocate)
			Eigen::internal::aligned_free(m_ptr);
	}

  protected:
	T* m_ptr;
	std::size_t m_size;
	bool m_deallocate;
};

#ifdef EIGEN_ALLOCA

template<typename Xpr,
		 int NbEvaluations,
		 bool MapExternalBuffer = nested_eval<Xpr, NbEvaluations>::Evaluate&& Xpr::MaxSizeAtCompileTime == Dynamic>
struct local_nested_eval_wrapper
{
	static const bool NeedExternalBuffer = false;
	typedef typename Xpr::Scalar Scalar;
	typedef typename nested_eval<Xpr, NbEvaluations>::type ObjectType;
	ObjectType object;

	EIGEN_DEVICE_FUNC
	local_nested_eval_wrapper(const Xpr& xpr, Scalar* ptr)
		: object(xpr)
	{
		EIGEN_UNUSED_VARIABLE(ptr);
		eigen_internal_assert(ptr == 0);
	}
};

template<typename Xpr, int NbEvaluations>
struct local_nested_eval_wrapper<Xpr, NbEvaluations, true>
{
	static const bool NeedExternalBuffer = true;
	typedef typename Xpr::Scalar Scalar;
	typedef typename plain_object_eval<Xpr>::type PlainObject;
	typedef Map<PlainObject, EIGEN_DEFAULT_ALIGN_BYTES> ObjectType;
	ObjectType object;

	EIGEN_DEVICE_FUNC
	local_nested_eval_wrapper(const Xpr& xpr, Scalar* ptr)
		: object(ptr == 0 ? reinterpret_cast<Scalar*>(Eigen::internal::aligned_malloc(sizeof(Scalar) * xpr.size()))
						  : ptr,
				 xpr.rows(),
				 xpr.cols())
		, m_deallocate(ptr == 0)
	{
		if (NumTraits<Scalar>::RequireInitialization && object.data())
			Eigen::internal::construct_elements_of_array(object.data(), object.size());
		object = xpr;
	}

	EIGEN_DEVICE_FUNC
	~local_nested_eval_wrapper()
	{
		if (NumTraits<Scalar>::RequireInitialization && object.data())
			Eigen::internal::destruct_elements_of_array(object.data(), object.size());
		if (m_deallocate)
			Eigen::internal::aligned_free(object.data());
	}

  private:
	bool m_deallocate;
};

#endif // EIGEN_ALLOCA

template<typename T>
class scoped_array : noncopyable
{
	T* m_ptr;

  public:
	explicit scoped_array(std::ptrdiff_t size) { m_ptr = new T[size]; }
	~scoped_array() { delete[] m_ptr; }
	T& operator[](std::ptrdiff_t i) { return m_ptr[i]; }
	const T& operator[](std::ptrdiff_t i) const { return m_ptr[i]; }
	T*& ptr() { return m_ptr; }
	const T* ptr() const { return m_ptr; }
	operator const T*() const { return m_ptr; }
};

template<typename T>
void
swap(scoped_array<T>& a, scoped_array<T>& b)
{
	std::swap(a.ptr(), b.ptr());
}

} // end namespace internal

/** \internal
 *
 * The macro ei_declare_aligned_stack_constructed_variable(TYPE,NAME,SIZE,BUFFER) declares, allocates,
 * and construct an aligned buffer named NAME of SIZE elements of type TYPE on the stack
 * if the size in bytes is smaller than EIGEN_STACK_ALLOCATION_LIMIT, and if stack allocation is supported by the
 * platform (currently, this is Linux, OSX and Visual Studio only). Otherwise the memory is allocated on the heap. The
 * allocated buffer is automatically deleted when exiting the scope of this declaration. If BUFFER is non null, then the
 * declared variable is simply an alias for BUFFER, and no allocation/deletion occurs. Here is an example: \code
 * {
 *   ei_declare_aligned_stack_constructed_variable(float,data,size,0);
 *   // use data[0] to data[size-1]
 * }
 * \endcode
 * The underlying stack allocation function can controlled with the EIGEN_ALLOCA preprocessor token.
 *
 * The macro ei_declare_local_nested_eval(XPR_T,XPR,N,NAME) is analogue to
 * \code
 *   typename internal::nested_eval<XPRT_T,N>::type NAME(XPR);
 * \endcode
 * with the advantage of using aligned stack allocation even if the maximal size of XPR at compile time is unknown.
 * This is accomplished through alloca if this later is supported and if the required number of bytes
 * is below EIGEN_STACK_ALLOCATION_LIMIT.
 */
#ifdef EIGEN_ALLOCA

#if EIGEN_DEFAULT_ALIGN_BYTES > 0
  // We always manually re-align the result of EIGEN_ALLOCA.
// If alloca is already aligned, the compiler should be smart enough to optimize away the re-alignment.
#define EIGEN_ALIGNED_ALLOCA(SIZE)                                                                                     \
	reinterpret_cast<void*>(                                                                                           \
		(internal::UIntPtr(EIGEN_ALLOCA(SIZE + EIGEN_DEFAULT_ALIGN_BYTES - 1)) + EIGEN_DEFAULT_ALIGN_BYTES - 1) &      \
		~(std::size_t(EIGEN_DEFAULT_ALIGN_BYTES - 1)))
#else
#define EIGEN_ALIGNED_ALLOCA(SIZE) EIGEN_ALLOCA(SIZE)
#endif

#define ei_declare_aligned_stack_constructed_variable(TYPE, NAME, SIZE, BUFFER)                                        \
	Eigen::internal::check_size_for_overflow<TYPE>(SIZE);                                                              \
	TYPE* NAME = (BUFFER) != 0 ? (BUFFER)                                                                              \
							   : reinterpret_cast<TYPE*>((sizeof(TYPE) * SIZE <= EIGEN_STACK_ALLOCATION_LIMIT)         \
															 ? EIGEN_ALIGNED_ALLOCA(sizeof(TYPE) * SIZE)               \
															 : Eigen::internal::aligned_malloc(sizeof(TYPE) * SIZE));  \
	Eigen::internal::aligned_stack_memory_handler<TYPE> EIGEN_CAT(NAME, _stack_memory_destructor)(                     \
		(BUFFER) == 0 ? NAME : 0, SIZE, sizeof(TYPE) * SIZE > EIGEN_STACK_ALLOCATION_LIMIT)

#define ei_declare_local_nested_eval(XPR_T, XPR, N, NAME)                                                              \
	Eigen::internal::local_nested_eval_wrapper<XPR_T, N> EIGEN_CAT(NAME, _wrapper)(                                    \
		XPR,                                                                                                           \
		reinterpret_cast<typename XPR_T::Scalar*>(                                                                     \
			((Eigen::internal::local_nested_eval_wrapper<XPR_T, N>::NeedExternalBuffer) &&                             \
			 ((sizeof(typename XPR_T::Scalar) * XPR.size()) <= EIGEN_STACK_ALLOCATION_LIMIT))                          \
				? EIGEN_ALIGNED_ALLOCA(sizeof(typename XPR_T::Scalar) * XPR.size())                                    \
				: 0));                                                                                                 \
	typename Eigen::internal::local_nested_eval_wrapper<XPR_T, N>::ObjectType NAME(EIGEN_CAT(NAME, _wrapper).object)

#else

#define ei_declare_aligned_stack_constructed_variable(TYPE, NAME, SIZE, BUFFER)                                        \
	Eigen::internal::check_size_for_overflow<TYPE>(SIZE);                                                              \
	TYPE* NAME =                                                                                                       \
		(BUFFER) != 0 ? BUFFER : reinterpret_cast<TYPE*>(Eigen::internal::aligned_malloc(sizeof(TYPE) * SIZE));        \
	Eigen::internal::aligned_stack_memory_handler<TYPE> EIGEN_CAT(NAME, _stack_memory_destructor)(                     \
		(BUFFER) == 0 ? NAME : 0, SIZE, true)

#define ei_declare_local_nested_eval(XPR_T, XPR, N, NAME)                                                              \
	typename Eigen::internal::nested_eval<XPR_T, N>::type NAME(XPR)

#endif

/*****************************************************************************
*** Implementation of EIGEN_MAKE_ALIGNED_OPERATOR_NEW [_IF]                ***
*****************************************************************************/

#if EIGEN_HAS_CXX17_OVERALIGN

// C++17 -> no need to bother about alignment anymore :)

#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign)
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar, Size)

#else

// HIP does not support new/delete on device.
#if EIGEN_MAX_ALIGN_BYTES != 0 && !defined(EIGEN_HIP_DEVICE_COMPILE)
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign)                                                          \
	EIGEN_DEVICE_FUNC                                                                                                  \
	void* operator new(std::size_t size, const std::nothrow_t&) EIGEN_NO_THROW                                         \
	{                                                                                                                  \
		EIGEN_TRY                                                                                                      \
		{                                                                                                              \
			return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size);                                    \
		}                                                                                                              \
		EIGEN_CATCH(...)                                                                                               \
		{                                                                                                              \
			return 0;                                                                                                  \
		}                                                                                                              \
	}
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)                                                               \
	EIGEN_DEVICE_FUNC                                                                                                  \
	void* operator new(std::size_t size)                                                                               \
	{                                                                                                                  \
		return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size);                                        \
	}                                                                                                                  \
	EIGEN_DEVICE_FUNC                                                                                                  \
	void* operator new[](std::size_t size)                                                                             \
	{                                                                                                                  \
		return Eigen::internal::conditional_aligned_malloc<NeedsToAlign>(size);                                        \
	}                                                                                                                  \
	EIGEN_DEVICE_FUNC                                                                                                  \
	void operator delete(void* ptr) EIGEN_NO_THROW                                                                     \
	{                                                                                                                  \
		Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr);                                                  \
	}                                                                                                                  \
	EIGEN_DEVICE_FUNC                                                                                                  \
	void operator delete[](void* ptr) EIGEN_NO_THROW                                                                   \
	{                                                                                                                  \
		Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr);                                                  \
	}                                                                                                                  \
	EIGEN_DEVICE_FUNC                                                                                                  \
	void operator delete(void* ptr, std::size_t /* sz */) EIGEN_NO_THROW                                               \
	{                                                                                                                  \
		Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr);                                                  \
	}                                                                                                                  \
	EIGEN_DEVICE_FUNC                                                                                                  \
	void operator delete[](void* ptr, std::size_t /* sz */) EIGEN_NO_THROW                                             \
	{                                                                                                                  \
		Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr);                                                  \
	}                                                                                                                  \
	/* in-place new and delete. since (at least afaik) there is no actual   */                                         \
	/* memory allocated we can safely let the default implementation handle */                                         \
	/* this particular case. */                                                                                        \
	EIGEN_DEVICE_FUNC                                                                                                  \
	static void* operator new(std::size_t size, void* ptr)                                                             \
	{                                                                                                                  \
		return ::operator new(size, ptr);                                                                              \
	}                                                                                                                  \
	EIGEN_DEVICE_FUNC                                                                                                  \
	static void* operator new[](std::size_t size, void* ptr)                                                           \
	{                                                                                                                  \
		return ::operator new[](size, ptr);                                                                            \
	}                                                                                                                  \
	EIGEN_DEVICE_FUNC                                                                                                  \
	void operator delete(void* memory, void* ptr) EIGEN_NO_THROW                                                       \
	{                                                                                                                  \
		return ::operator delete(memory, ptr);                                                                         \
	}                                                                                                                  \
	EIGEN_DEVICE_FUNC                                                                                                  \
	void operator delete[](void* memory, void* ptr) EIGEN_NO_THROW                                                     \
	{                                                                                                                  \
		return ::operator delete[](memory, ptr);                                                                       \
	}                                                                                                                  \
	/* nothrow-new (returns zero instead of std::bad_alloc) */                                                         \
	EIGEN_MAKE_ALIGNED_OPERATOR_NEW_NOTHROW(NeedsToAlign)                                                              \
	EIGEN_DEVICE_FUNC                                                                                                  \
	void operator delete(void* ptr, const std::nothrow_t&) EIGEN_NO_THROW                                              \
	{                                                                                                                  \
		Eigen::internal::conditional_aligned_free<NeedsToAlign>(ptr);                                                  \
	}                                                                                                                  \
	typedef void eigen_aligned_operator_new_marker_type;
#else
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsToAlign)
#endif

#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(true)
#define EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar, Size)                                       \
	EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(                                                                                \
		bool(((Size) != Eigen::Dynamic) &&                                                                             \
			 (((EIGEN_MAX_ALIGN_BYTES >= 16) && ((sizeof(Scalar) * (Size)) % (EIGEN_MAX_ALIGN_BYTES) == 0)) ||         \
			  ((EIGEN_MAX_ALIGN_BYTES >= 32) && ((sizeof(Scalar) * (Size)) % (EIGEN_MAX_ALIGN_BYTES / 2) == 0)) ||     \
			  ((EIGEN_MAX_ALIGN_BYTES >= 64) && ((sizeof(Scalar) * (Size)) % (EIGEN_MAX_ALIGN_BYTES / 4) == 0)))))

#endif

/****************************************************************************/

/** \class aligned_allocator
 * \ingroup Core_Module
 *
 * \brief STL compatible allocator to use with types requiring a non standrad alignment.
 *
 * The memory is aligned as for dynamically aligned matrix/array types such as MatrixXd.
 * By default, it will thus provide at least 16 bytes alignment and more in following cases:
 *  - 32 bytes alignment if AVX is enabled.
 *  - 64 bytes alignment if AVX512 is enabled.
 *
 * This can be controlled using the \c EIGEN_MAX_ALIGN_BYTES macro as documented
 * \link TopicPreprocessorDirectivesPerformance there \endlink.
 *
 * Example:
 * \code
 * // Matrix4f requires 16 bytes alignment:
 * std::map< int, Matrix4f, std::less<int>,
 *           aligned_allocator<std::pair<const int, Matrix4f> > > my_map_mat4;
 * // Vector3f does not require 16 bytes alignment, no need to use Eigen's allocator:
 * std::map< int, Vector3f > my_map_vec3;
 * \endcode
 *
 * \sa \blank \ref TopicStlContainers.
 */
template<class T>
class aligned_allocator : public std::allocator<T>
{
  public:
	typedef std::size_t size_type;
	typedef std::ptrdiff_t difference_type;
	typedef T* pointer;
	typedef const T* const_pointer;
	typedef T& reference;
	typedef const T& const_reference;
	typedef T value_type;

	template<class U>
	struct rebind
	{
		typedef aligned_allocator<U> other;
	};

	aligned_allocator()
		: std::allocator<T>()
	{
	}

	aligned_allocator(const aligned_allocator& other)
		: std::allocator<T>(other)
	{
	}

	template<class U>
	aligned_allocator(const aligned_allocator<U>& other)
		: std::allocator<T>(other)
	{
	}

	~aligned_allocator() {}

#if EIGEN_COMP_GNUC_STRICT && EIGEN_GNUC_AT_LEAST(7, 0)
	// In gcc std::allocator::max_size() is bugged making gcc triggers a warning:
	// eigen/Eigen/src/Core/util/Memory.h:189:12: warning: argument 1 value '18446744073709551612' exceeds maximum
	// object size 9223372036854775807 See https://gcc.gnu.org/bugzilla/show_bug.cgi?id=87544
	size_type max_size() const { return (std::numeric_limits<std::ptrdiff_t>::max)() / sizeof(T); }
#endif

	pointer allocate(size_type num, const void* /*hint*/ = 0)
	{
		internal::check_size_for_overflow<T>(num);
		return static_cast<pointer>(internal::aligned_malloc(num * sizeof(T)));
	}

	void deallocate(pointer p, size_type /*num*/) { internal::aligned_free(p); }
};

//---------- Cache sizes ----------

#if !defined(EIGEN_NO_CPUID)
#if EIGEN_COMP_GNUC && EIGEN_ARCH_i386_OR_x86_64
#if defined(__PIC__) && EIGEN_ARCH_i386
// Case for x86 with PIC
#define EIGEN_CPUID(abcd, func, id)                                                                                    \
	__asm__ __volatile__("xchgl %%ebx, %k1;cpuid; xchgl %%ebx,%k1"                                                     \
						 : "=a"(abcd[0]), "=&r"(abcd[1]), "=c"(abcd[2]), "=d"(abcd[3])                                 \
						 : "a"(func), "c"(id));
#elif defined(__PIC__) && EIGEN_ARCH_x86_64
// Case for x64 with PIC. In theory this is only a problem with recent gcc and with medium or large code model, not with
// the default small code model. However, we cannot detect which code model is used, and the xchg overhead is negligible
// anyway.
#define EIGEN_CPUID(abcd, func, id)                                                                                    \
	__asm__ __volatile__("xchg{q}\t{%%}rbx, %q1; cpuid; xchg{q}\t{%%}rbx, %q1"                                         \
						 : "=a"(abcd[0]), "=&r"(abcd[1]), "=c"(abcd[2]), "=d"(abcd[3])                                 \
						 : "0"(func), "2"(id));
#else
// Case for x86_64 or x86 w/o PIC
#define EIGEN_CPUID(abcd, func, id)                                                                                    \
	__asm__ __volatile__("cpuid" : "=a"(abcd[0]), "=b"(abcd[1]), "=c"(abcd[2]), "=d"(abcd[3]) : "0"(func), "2"(id));
#endif
#elif EIGEN_COMP_MSVC
#if (EIGEN_COMP_MSVC > 1500) && EIGEN_ARCH_i386_OR_x86_64
#define EIGEN_CPUID(abcd, func, id) __cpuidex((int*)abcd, func, id)
#endif
#endif
#endif

namespace internal {

#ifdef EIGEN_CPUID

inline bool
cpuid_is_vendor(int abcd[4], const int vendor[3])
{
	return abcd[1] == vendor[0] && abcd[3] == vendor[1] && abcd[2] == vendor[2];
}

inline void
queryCacheSizes_intel_direct(int& l1, int& l2, int& l3)
{
	int abcd[4];
	l1 = l2 = l3 = 0;
	int cache_id = 0;
	int cache_type = 0;
	do {
		abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
		EIGEN_CPUID(abcd, 0x4, cache_id);
		cache_type = (abcd[0] & 0x0F) >> 0;
		if (cache_type == 1 || cache_type == 3) // data or unified cache
		{
			int cache_level = (abcd[0] & 0xE0) >> 5;	   // A[7:5]
			int ways = (abcd[1] & 0xFFC00000) >> 22;	   // B[31:22]
			int partitions = (abcd[1] & 0x003FF000) >> 12; // B[21:12]
			int line_size = (abcd[1] & 0x00000FFF) >> 0;   // B[11:0]
			int sets = (abcd[2]);						   // C[31:0]

			int cache_size = (ways + 1) * (partitions + 1) * (line_size + 1) * (sets + 1);

			switch (cache_level) {
				case 1:
					l1 = cache_size;
					break;
				case 2:
					l2 = cache_size;
					break;
				case 3:
					l3 = cache_size;
					break;
				default:
					break;
			}
		}
		cache_id++;
	} while (cache_type > 0 && cache_id < 16);
}

inline void
queryCacheSizes_intel_codes(int& l1, int& l2, int& l3)
{
	int abcd[4];
	abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
	l1 = l2 = l3 = 0;
	EIGEN_CPUID(abcd, 0x00000002, 0);
	unsigned char* bytes = reinterpret_cast<unsigned char*>(abcd) + 2;
	bool check_for_p2_core2 = false;
	for (int i = 0; i < 14; ++i) {
		switch (bytes[i]) {
			case 0x0A:
				l1 = 8;
				break; // 0Ah   data L1 cache, 8 KB, 2 ways, 32 byte lines
			case 0x0C:
				l1 = 16;
				break; // 0Ch   data L1 cache, 16 KB, 4 ways, 32 byte lines
			case 0x0E:
				l1 = 24;
				break; // 0Eh   data L1 cache, 24 KB, 6 ways, 64 byte lines
			case 0x10:
				l1 = 16;
				break; // 10h   data L1 cache, 16 KB, 4 ways, 32 byte lines (IA-64)
			case 0x15:
				l1 = 16;
				break; // 15h   code L1 cache, 16 KB, 4 ways, 32 byte lines (IA-64)
			case 0x2C:
				l1 = 32;
				break; // 2Ch   data L1 cache, 32 KB, 8 ways, 64 byte lines
			case 0x30:
				l1 = 32;
				break; // 30h   code L1 cache, 32 KB, 8 ways, 64 byte lines
			case 0x60:
				l1 = 16;
				break; // 60h   data L1 cache, 16 KB, 8 ways, 64 byte lines, sectored
			case 0x66:
				l1 = 8;
				break; // 66h   data L1 cache, 8 KB, 4 ways, 64 byte lines, sectored
			case 0x67:
				l1 = 16;
				break; // 67h   data L1 cache, 16 KB, 4 ways, 64 byte lines, sectored
			case 0x68:
				l1 = 32;
				break; // 68h   data L1 cache, 32 KB, 4 ways, 64 byte lines, sectored
			case 0x1A:
				l2 = 96;
				break; // code and data L2 cache, 96 KB, 6 ways, 64 byte lines (IA-64)
			case 0x22:
				l3 = 512;
				break; // code and data L3 cache, 512 KB, 4 ways (!), 64 byte lines, dual-sectored
			case 0x23:
				l3 = 1024;
				break; // code and data L3 cache, 1024 KB, 8 ways, 64 byte lines, dual-sectored
			case 0x25:
				l3 = 2048;
				break; // code and data L3 cache, 2048 KB, 8 ways, 64 byte lines, dual-sectored
			case 0x29:
				l3 = 4096;
				break; // code and data L3 cache, 4096 KB, 8 ways, 64 byte lines, dual-sectored
			case 0x39:
				l2 = 128;
				break; // code and data L2 cache, 128 KB, 4 ways, 64 byte lines, sectored
			case 0x3A:
				l2 = 192;
				break; // code and data L2 cache, 192 KB, 6 ways, 64 byte lines, sectored
			case 0x3B:
				l2 = 128;
				break; // code and data L2 cache, 128 KB, 2 ways, 64 byte lines, sectored
			case 0x3C:
				l2 = 256;
				break; // code and data L2 cache, 256 KB, 4 ways, 64 byte lines, sectored
			case 0x3D:
				l2 = 384;
				break; // code and data L2 cache, 384 KB, 6 ways, 64 byte lines, sectored
			case 0x3E:
				l2 = 512;
				break; // code and data L2 cache, 512 KB, 4 ways, 64 byte lines, sectored
			case 0x40:
				l2 = 0;
				break; // no integrated L2 cache (P6 core) or L3 cache (P4 core)
			case 0x41:
				l2 = 128;
				break; // code and data L2 cache, 128 KB, 4 ways, 32 byte lines
			case 0x42:
				l2 = 256;
				break; // code and data L2 cache, 256 KB, 4 ways, 32 byte lines
			case 0x43:
				l2 = 512;
				break; // code and data L2 cache, 512 KB, 4 ways, 32 byte lines
			case 0x44:
				l2 = 1024;
				break; // code and data L2 cache, 1024 KB, 4 ways, 32 byte lines
			case 0x45:
				l2 = 2048;
				break; // code and data L2 cache, 2048 KB, 4 ways, 32 byte lines
			case 0x46:
				l3 = 4096;
				break; // code and data L3 cache, 4096 KB, 4 ways, 64 byte lines
			case 0x47:
				l3 = 8192;
				break; // code and data L3 cache, 8192 KB, 8 ways, 64 byte lines
			case 0x48:
				l2 = 3072;
				break; // code and data L2 cache, 3072 KB, 12 ways, 64 byte lines
			case 0x49:
				if (l2 != 0)
					l3 = 4096;
				else {
					check_for_p2_core2 = true;
					l3 = l2 = 4096;
				}
				break; // code and data L3 cache, 4096 KB, 16 ways, 64 byte lines (P4) or L2 for core2
			case 0x4A:
				l3 = 6144;
				break; // code and data L3 cache, 6144 KB, 12 ways, 64 byte lines
			case 0x4B:
				l3 = 8192;
				break; // code and data L3 cache, 8192 KB, 16 ways, 64 byte lines
			case 0x4C:
				l3 = 12288;
				break; // code and data L3 cache, 12288 KB, 12 ways, 64 byte lines
			case 0x4D:
				l3 = 16384;
				break; // code and data L3 cache, 16384 KB, 16 ways, 64 byte lines
			case 0x4E:
				l2 = 6144;
				break; // code and data L2 cache, 6144 KB, 24 ways, 64 byte lines
			case 0x78:
				l2 = 1024;
				break; // code and data L2 cache, 1024 KB, 4 ways, 64 byte lines
			case 0x79:
				l2 = 128;
				break; // code and data L2 cache, 128 KB, 8 ways, 64 byte lines, dual-sectored
			case 0x7A:
				l2 = 256;
				break; // code and data L2 cache, 256 KB, 8 ways, 64 byte lines, dual-sectored
			case 0x7B:
				l2 = 512;
				break; // code and data L2 cache, 512 KB, 8 ways, 64 byte lines, dual-sectored
			case 0x7C:
				l2 = 1024;
				break; // code and data L2 cache, 1024 KB, 8 ways, 64 byte lines, dual-sectored
			case 0x7D:
				l2 = 2048;
				break; // code and data L2 cache, 2048 KB, 8 ways, 64 byte lines
			case 0x7E:
				l2 = 256;
				break; // code and data L2 cache, 256 KB, 8 ways, 128 byte lines, sect. (IA-64)
			case 0x7F:
				l2 = 512;
				break; // code and data L2 cache, 512 KB, 2 ways, 64 byte lines
			case 0x80:
				l2 = 512;
				break; // code and data L2 cache, 512 KB, 8 ways, 64 byte lines
			case 0x81:
				l2 = 128;
				break; // code and data L2 cache, 128 KB, 8 ways, 32 byte lines
			case 0x82:
				l2 = 256;
				break; // code and data L2 cache, 256 KB, 8 ways, 32 byte lines
			case 0x83:
				l2 = 512;
				break; // code and data L2 cache, 512 KB, 8 ways, 32 byte lines
			case 0x84:
				l2 = 1024;
				break; // code and data L2 cache, 1024 KB, 8 ways, 32 byte lines
			case 0x85:
				l2 = 2048;
				break; // code and data L2 cache, 2048 KB, 8 ways, 32 byte lines
			case 0x86:
				l2 = 512;
				break; // code and data L2 cache, 512 KB, 4 ways, 64 byte lines
			case 0x87:
				l2 = 1024;
				break; // code and data L2 cache, 1024 KB, 8 ways, 64 byte lines
			case 0x88:
				l3 = 2048;
				break; // code and data L3 cache, 2048 KB, 4 ways, 64 byte lines (IA-64)
			case 0x89:
				l3 = 4096;
				break; // code and data L3 cache, 4096 KB, 4 ways, 64 byte lines (IA-64)
			case 0x8A:
				l3 = 8192;
				break; // code and data L3 cache, 8192 KB, 4 ways, 64 byte lines (IA-64)
			case 0x8D:
				l3 = 3072;
				break; // code and data L3 cache, 3072 KB, 12 ways, 128 byte lines (IA-64)

			default:
				break;
		}
	}
	if (check_for_p2_core2 && l2 == l3)
		l3 = 0;
	l1 *= 1024;
	l2 *= 1024;
	l3 *= 1024;
}

inline void
queryCacheSizes_intel(int& l1, int& l2, int& l3, int max_std_funcs)
{
	if (max_std_funcs >= 4)
		queryCacheSizes_intel_direct(l1, l2, l3);
	else if (max_std_funcs >= 2)
		queryCacheSizes_intel_codes(l1, l2, l3);
	else
		l1 = l2 = l3 = 0;
}

inline void
queryCacheSizes_amd(int& l1, int& l2, int& l3)
{
	int abcd[4];
	abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;

	// First query the max supported function.
	EIGEN_CPUID(abcd, 0x80000000, 0);
	if (static_cast<numext::uint32_t>(abcd[0]) >= static_cast<numext::uint32_t>(0x80000006)) {
		EIGEN_CPUID(abcd, 0x80000005, 0);
		l1 = (abcd[2] >> 24) * 1024; // C[31:24] = L1 size in KB
		abcd[0] = abcd[1] = abcd[2] = abcd[3] = 0;
		EIGEN_CPUID(abcd, 0x80000006, 0);
		l2 = (abcd[2] >> 16) * 1024;					 // C[31;16] = l2 cache size in KB
		l3 = ((abcd[3] & 0xFFFC000) >> 18) * 512 * 1024; // D[31;18] = l3 cache size in 512KB
	} else {
		l1 = l2 = l3 = 0;
	}
}
#endif

/** \internal
 * Queries and returns the cache sizes in Bytes of the L1, L2, and L3 data caches respectively */
inline void
queryCacheSizes(int& l1, int& l2, int& l3)
{
#ifdef EIGEN_CPUID
	int abcd[4];
	const int GenuineIntel[] = { 0x756e6547, 0x49656e69, 0x6c65746e };
	const int AuthenticAMD[] = { 0x68747541, 0x69746e65, 0x444d4163 };
	const int AMDisbetter_[] = { 0x69444d41, 0x74656273, 0x21726574 }; // "AMDisbetter!"

	// identify the CPU vendor
	EIGEN_CPUID(abcd, 0x0, 0);
	int max_std_funcs = abcd[0];
	if (cpuid_is_vendor(abcd, GenuineIntel))
		queryCacheSizes_intel(l1, l2, l3, max_std_funcs);
	else if (cpuid_is_vendor(abcd, AuthenticAMD) || cpuid_is_vendor(abcd, AMDisbetter_))
		queryCacheSizes_amd(l1, l2, l3);
	else
		// by default let's use Intel's API
		queryCacheSizes_intel(l1, l2, l3, max_std_funcs);

		// here is the list of other vendors:
		//   ||cpuid_is_vendor(abcd,"VIA VIA VIA ")
		//   ||cpuid_is_vendor(abcd,"CyrixInstead")
		//   ||cpuid_is_vendor(abcd,"CentaurHauls")
		//   ||cpuid_is_vendor(abcd,"GenuineTMx86")
		//   ||cpuid_is_vendor(abcd,"TransmetaCPU")
		//   ||cpuid_is_vendor(abcd,"RiseRiseRise")
		//   ||cpuid_is_vendor(abcd,"Geode by NSC")
		//   ||cpuid_is_vendor(abcd,"SiS SiS SiS ")
		//   ||cpuid_is_vendor(abcd,"UMC UMC UMC ")
		//   ||cpuid_is_vendor(abcd,"NexGenDriven")
#else
	l1 = l2 = l3 = -1;
#endif
}

/** \internal
 * \returns the size in Bytes of the L1 data cache */
inline int
queryL1CacheSize()
{
	int l1(-1), l2, l3;
	queryCacheSizes(l1, l2, l3);
	return l1;
}

/** \internal
 * \returns the size in Bytes of the L2 or L3 cache if this later is present */
inline int
queryTopLevelCacheSize()
{
	int l1, l2(-1), l3(-1);
	queryCacheSizes(l1, l2, l3);
	return (std::max)(l2, l3);
}

} // end namespace internal

} // end namespace Eigen

#endif // EIGEN_MEMORY_H
